Integral attacks on reduced-round Deoxys-BC and RAIN algorithms

Considering the impact of tweakeys on tweakable block cipher algorithms, achieved integral attacks on Deoxys-BC and RAIN algorithms by combining zero-correlation linear cryptanalysis with integral attacks and utilizing partial-sum technique. 176 types of 5.5-round zero-correlation linear distinguishers for Deoxys-BC-256 and 176 types of 6.5-round zero-correlation linear distinguishers for Deoxys-BC-384 were constructed by taking the mask propagation rules of tweakeys into consideration. Based on the relationship between zero-correlation linear distinguishers and integral distinguishers, achieved 10-round and 12-round integral attacks on the two versions of Deoxys-BC respectively by combining equivalent key technique. Then, 48 types of 6-round zero-correlation linear distinguishers for RAIN algorithm were constructed, and converted them into 6-round integral distinguishers. Without considering the whitening key, 10-round integral attacks were achieved on both versions of RAIN algorithm. The results show that the complexities of the proposed attack scheme are significantly reduced compared with those of the existing ones.